How to predict Q-values based on stack of frames
You do not output the batch of Q-values. Input frame stacking is needed to gain full observability of the environment. In your case the output would be 6 elements for your current frame. If $F$ is a frame then you would stack 4 frames $[F_{k-3}, F_{k-2}, F_{k-1}, F_k]$ and the output would be 6 Q-values for frame $F_k$.